基于张量函数的双变量弹塑性本构理论和实验研究

In this project, we will construct the non-linear elastoplasticity constitutive equation deduced from the tensor functions which has two variables of finite strain and temperature. Compared with existing constitutive equation theory, such as phenomenological and crystallographic theory, the elastoplasticity constant of the constitutive equation is complete, irreducible. It is not only applicable to the specific conditions and the individual materials, and can describe the physical characteristics of a large class of materials. The other aim of this project is to propose a novel spherical failure criterion. The new criterion, which is proposed based on the tensor invariant, overcomes the defects that the yield surface is not closed, it is more reasonable and universal. This theoretical result could be used to study the mechanical properties of the high-temperature Nickel-base materials in high ultra-super power generation. At the same time, experimental studies of Nickel-base materials will be conducted, by design, improved high-temperature test methods and means to obtain the key mechanical index reflecting the properties of nickel-based materials. This can provide a basis for the design and application of nickel-based materials effectively. At the same time, we will compare the experimental data and theoretical results, further proof of the correctness of the theoretical results. Many complex mechanical experiments are restricted by equipment or technically. the theoretical constitutive model will be used in the finite element software for the simulation research, and thus to obtain the elastic-plastic mechanical properties critical data of the high-temperature materials，which can not be obtained with the experimental method. The intending results could be used to promote the application quality of high-temperature materials in high ultra-super power generation.

本课题直接从张量函数出发建立基于有限应变、温度的双变量弹塑性非线性本构理论。应用该理论得到的本构方程与目前文献中应用唯象理论和晶体滑移理论所得方程相比，其材料弹塑性常数是完备的、不可约的。它不仅适用于特定工况和个体材料，而且可以描述一大类材料的物理特性。本课题将进一步导出材料新的球面屈服准则，新准则克服了屈服面不封闭的缺陷，更具有合理性、普适性。以高超超燃煤机组中镍基高温材料应用研究为背景，开展实验研究，通过设计、改进高温试验方法和手段，更有效地获取镍基材料某些关键力学性能指标，将实验数据与理论成果比较，进一步证明理论成果的正确性，并为镍基材料的设计和应用提供依据。许多复杂的受力实验，在设备、技术上都受到限制，将本课题最新本构模型植入商业有限元软件，进行数值仿真研究，进一步获取高温材料不具备实验条件的其它弹塑性力学性能关键数据，提升我国高超超临界燃煤机组高温材料的应用提供支持。

随着高温新型材料的应用，建立考虑温度影响的热弹塑性本构理论成为当前力学、材料学研究的热点问题之一。目前，高温材料本构关系的研究大多基于唯象理论,根据具体材料实验结果构造出的本构方程大多不具有普适性。本项目直接从张量函数出发建立基于有限应变、温度增量为变量的弹塑性非线性本构理论，推导出用张量不变量、标量不变量表示的本构方程，并且证明材料弹塑性常数是完备的，不可约的。方程可以描述一大类材料的力学特性。项目获得以下研究结果：（1）在研究各向同性、横观各向同性弹塑性张量分量个数及其对称性的基础上，建立了以张量、标量不变量形式表示的各向同性、横观各向同性非线性弹塑性本构方程。考虑温度影响，将应变分量分解为载荷作用与温度作用两部分，得到完备的不可约的各向同性、横观各向同性非线性热弹塑性本构方程。利用MATLAB软件，将本构方程同多晶镁、镍基高温合金DZ125材料的实验结果进行拟合分析，拟合结果与实验结果具有良好的一致性。（2）从张量方程出发，应用张量表示定理，推导得到不变量表示的正交各向异性材料热弹塑性本构方程，本构方程是完备的不可约的。（3）将非线性热本构方程应用于壳体热屈曲研究。推导得到了正交曲线坐标系下任意形状薄壳的稳定性方程组。在非线性热本构理论下，采用伽辽金法和里兹法计算了简支球壳分别考虑均布外压和温度作用下的热屈曲荷载，分析了薄球壳厚度变化引起的临界温度变化趋势和临界压力的变化趋势；在线性、非线性热本构理论下，分析了功能梯度材料薄球壳温度变化引起的临界压力变化趋势；分析了温度非线性对临界压力的影响；编著专著《壳体热屈曲理论》。（4）在研究弹塑性常数个数及其规律当中发现了素数矩阵分布规律，在总结规律的基础上，完成素数矩阵的研究，编著出版专著《矩阵数论》。